TY  - BOOK
AU  - Alonso-Gutiérrez,David
AU  - Bastero,Jesús
ED  - SpringerLink (Online service)
TI  - Approaching the Kannan-Lovász-Simonovits and Variance Conjectures
T2  - Lecture Notes in Mathematics,
SN  - 9783319132631
AV  - QA319-329.9 
U1  - 515.7 23
PY  - 2015///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - mathematics
KW  - Functional analysis
KW  - Convex geometry
KW  - Discrete geometry
KW  - Probabilities
KW  - Mathematics
KW  - Functional Analysis
KW  - Convex and Discrete Geometry
KW  - Probability Theory and Stochastic Processes
N1  - The Conjectures -- Main Examples -- Relating the Conjectures -- Appendix -- Index
N2  - Focusing on two central conjectures from the field of Asymptotic Geometric Analysis, the Kannan-Lovász-Simonovits spectral gap conjecture and the variance conjecture, these Lecture Notes present the theory in an accessible way, so that interested readers, even those who are not experts in the field, will be able to appreciate the topics treated. Employing a style suitable for professionals with little background in analysis, geometry or probability, the work goes directly to the connection between isoperimetric-type inequalities and functional inequalities, allowing readers to quickly access the core of these conjectures. In addition, four recent and important results concerning this theory are presented. The first two are theorems attributed to Eldan-Klartag and Ball-Nguyen, which relate the variance and the KLS conjectures, respectively, to the hyperplane conjecture. The remaining two present in detail the main ideas needed to prove the best known estimate for the thin-shell width given by Guédon-Milman, and an approach to Eldan’s work on the connection between the thin-shell width and the KLS conjecture
UR  - http://dx.doi.org/10.1007/978-3-319-13263-1
ER  -